Probability Distribution Function of Cosmological Density Fluctuations from a Gaussian Initial Condition: Comparison of One-Point and Two-Point Lognormal Model Predictions with N-Body Simulations
Probability Distribution Function of Cosmological Density Fluctuations from a Gaussian Initial Condition: Comparison of One-Point and Two-Point Lognormal Model Predictions with N-Body Simulations
复制标题
高斯初始条件下宇宙密度涨落的概率分布函数：单点和两点对数正态模型预测与 N 体模拟的比较
DOI：
10.1086/323227
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Y. Suto
中科院分区：
文献类型：
--
作者：
I. Kayo;A. Taruya;Y. Suto
本文定量研究了在高斯初始条件下N体模拟中宇宙学非线性密度涨落的概率分布函数。特别是，我们研究的有效性和局限性的一点和两点对数正态PDF模型对那些直接估计的模拟。我们发现，一点对数正态概率密度函数非常精确地描述了宇宙学密度分布，即使在非线性区域（均方根方差σnl <$4，超密度δ <$100）。此外，两点对数正态PDF也与模拟数据从线性到相当非线性的区域吻合良好，而当δ =-0.5时，它们与模拟数据略有偏离。因此，对数正态概率密度函数可以作为一个有用的宇宙学密度涨落的经验模型。虽然这一结论对密度波动P（k）的基本功率谱的形状相当不敏感，但在大尺度上具有相当大功率的模型，即，n d ln P（k）/d ln k-1，用对数正态PDF更好地描述。另一方面，我们注意到，初始和演化密度场的一对一映射，与对数正态模型一致，即使在平均值上也不近似它们的相互关联的广泛分布。因此，现象学对数正态PDF近似的起源仍然有待理解。
We quantitatively study the probability distribution function (PDF) of cosmological nonlinear density fluctuations from N-body simulations with a Gaussian initial condition. In particular, we examine the validity and limitations of one-point and two-point lognormal PDF models against those directly estimated from the simulations. We find that the one-point lognormal PDF very accurately describes the cosmological density distribution even in the nonlinear regime (rms variance σnl ≲ 4, overdensity δ ≲ 100). Furthermore, the two-point lognormal PDFs are also in good agreement with the simulation data from linear to fairly nonlinear regimes, while they deviate slightly from the simulation data for δ ≲ -0.5. Thus, the lognormal PDF can be used as a useful empirical model for the cosmological density fluctuations. While this conclusion is fairly insensitive to the shape of the underlying power spectrum of density fluctuations P(k), models with substantial power on large scales, i.e., n ≡ d ln P(k)/d ln k ≲ -1, are better described by the lognormal PDF. On the other hand, we note that the one-to-one mapping of the initial and evolved density fields, consistent with the lognormal model, does not approximate the broad distribution of their mutual correlation even on average. Thus, the origin of the phenomenological lognormal PDF approximation still remains to be understood.